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Homework Help: Projectile motion: determine launch angle

  1. Jan 15, 2014 #1
    1. The problem statement, all variables and given/known data

    A cannon is supported one meter above the top of a 20 degree declining slope of length 200m. The cannon has a launch velocity of 55m/s. There is a ball halfway down this slope moving at a constant velocity of 20m/s.

    -Determine the angle [itex]\Theta[/itex] required for the projectile to hit the bottom of the hill within one degree.
    -How long does the projectile take to hit the bottom of the hill?
    -There is a target moving at a constant velocity of 20m/s down the hill. How long should you delay firing to hit the target as it reaches the bottom of the hill?
    -Find the maximum distance this projectile can travel as measured from the bottom of the hill.

    2. Relevant equations


    3. The attempt at a solution

    I have tried using all of the two-dimensional kinematics equations with some success but the problem is that [itex]\Theta[/itex] is unknown so I can't find t or v[itex]_{fy}[/itex].

    My best attempts are as so:

    The diagram for the problem is attached.
    Either it is algebra more complicated than I am used to or I am missing something very simple. I am confident that if I could solve for [itex]\Theta[/itex] OR t I could finish the problem easily. I can't seem to get a solveable equation. Thank you for your help and I apologize if there are syntax errors as I am a first time user.

    Attached Files:

    Last edited: Jan 15, 2014
  2. jcsd
  3. Jan 15, 2014 #2
    There is inconsistency , the questions on the attachment and the problem statement you provided . I would like to help you but there are some ambiguity .
  4. Jan 15, 2014 #3
    I apologize for that. I just updated the post to match the wording of the diagram exactly. I have continued to work on this problem and used a few pages of paper, but still have not been able to find a way to solve for theta.
  5. Jan 15, 2014 #4
    You have to find the range in terms of the initial angle then try to optimize it . That is how I solved it . You have to think why one needs an optimization approach to solve this problem.
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